Luke has $21 more than rachel and $48 more than daniel. altogether they have $168. how much does luke have?

Let Luke be represented as L , rachel be represented as R and daniel be represented as D

As per the statement: Luke has $21 more than rachel and $48 more than daniel

⇒  and L = 48+D    

equate these two we get;

21 + R = 48 + D

we can write this as;

R = 48+D -21

R = 27 +D                    ......[1]                

Also, it is given that altogether they have $168.

⇒              .....[2]

Substitute the value of L=21+R in equation [2] we have;

Combine like terms;

Subtract 21 from both sides we get;

2R+D= 147                           ......[3]

Substitute the value of equation [1] in [3] we get;

2(27+D)+D = 147

Using distributive property;

54 + 2D +D = 147

Combine like terms;

54 +3D =147

Subtract 54 from both sides we get;

3D = 93

Divide both sides by 3 we get;

D = $31

Now, substitute this value of D in L = 48+D we have;

L = 48 + 31 = $79

Therefore, $79 does Luke have.